Uniformly Most Powerful Test - Setting

Setting

Let denote a random vector (corresponding to the measurements), taken from a parametrized family of probability density functions or probability mass functions, which depends on the unknown deterministic parameter . The parameter space is partitioned into two disjoint sets and . Let denote the hypothesis that, and let denote the hypothesis that . The binary test of hypotheses is performed using a test function .

\phi(x) = \begin{cases} 1 & \text{if } x \in R \\ 0 & \text{if } x \in A \end{cases}

meaning that is in force if the measurement and that is in force if the measurement . Note that is a disjoint covering of the measurement space.

Read more about this topic:  Uniformly Most Powerful Test

Famous quotes containing the word setting:

    “High from the summit of a craggy cliff,
    Hung o’er the deep, such as amazing frowns
    On utmost Kilda’s shore, whose lonely race
    Resign the setting sun to Indian worlds,
    The royal eagle draws his vigorous young”
    —James Thomson (1700–1748)

    “The doctrine of those who have denied that certainty could be attained at all, has some agreement with my way of proceeding at the first setting out; but they end in being infinitely separated and opposed. For the holders of that doctrine assert simply that nothing can be known; I also assert that not much can be known in nature by the way which is now in use. But then they go on to destroy the authority of the senses and understanding; whereas I proceed to devise helps for the same.”
    —Francis Bacon (1560–1626)

    “The setting was really perfect for a brisk bubbling murder....”
    —Vladimir Nabokov (1899–1977)